ds di = g[K - S] Where g is a positive constant, S denotes the stock and K is the carrying capacity of the resource. Tastes are given by the following utility function. 1 = HaMl-a Where H is the harvest from the renewable resource, M is consumption of manufactures, and "a" is a positive fraction less than one. There is a representative agent who supplies L unitsof labor at each moment in time. All markets are competitive, and there is no regulation in the resource sector. The production functions for harvesting and manufacturing are given by: H = QLAS M - LM a) Suppose we start in autarky. Solve for the steady state resource stock in autarky, steady state autarky relative prices (let p = pp/pw), and steady state consumption of both the harvest good and manufactures. What parameter restrictions, if any, do you need to impose to ensure the resource is not driven to extinction? b) Denote the autarky steady state resource stock by $4 and the associated autarky rel- ative price by p. Suppose we start with an initial stock S(0) > $4. Show using two diagrams the economy's transition towards its autarkic steady state. One diagram should show a couple of temporary Ricardian equilibria; the other should plot ds/di against S and describe the dynamics. Is this steady state unique? c) Now open this economy up to trade at a fixed world relative price indicated by p . For what set of relative prices p" would this economy specialize in only the production of the Harvest good in steady state? For what set of relative prices p' would this economy diversify and produce both goods, but export the Harvest good in steady state? Does this economy gain from trade? If so, when? Why